Number of elements where n belongs to N and Sn Intersection Tn is phi

For , Let and

Then the number of elements in the set is

(A) 0
(B) 2
(C) 3
(D) 4

Solution:

Tip for solving this question:

Firstly Identify the given sets

According to the set type, apply intersection properties to find no. of elements.

Step 1 of 2:

Let z = x + iy

Given,

Represents a circle with centre

Also,

Represents a circle with centre

Step 2 of 2:

We have

So, distance between centre >

{}

Here, n = 1, 2, 3, 4 only satisfies the above equation.

Therefore, No. of elements in sets = 4

Final Answer:

Hence, Option (D) is correct.